This paper describes a complexity-effective design of auditory compensation, which is the most important building block in digital hearing aids. A multi-rate architecture and the filter bank design thereof are proposed to significantly reduce the data rates of the band-limited channels and thus the computational complexity. Several optimizations are discussed to further simplify the implementation of the dynamic range compressors in the multi-rate auditory compensation. In an 18-band 24-KHz digital hearing aid, 94% multiplications and additions are saved from a straightforward filter bank design. Moreover, the computation and memory requirements of the dynamic range compressor of each band are reduced to only 16% and 1% respectively.